**Author**: Paul Frank Baum,Ralf Meyer,Rubén Sánchez-García,Marco Schlichting,Bertrand Toën

**Publisher:**Springer Science & Business Media

**ISBN:**3642157076

**Category:**Mathematics

**Page:**308

**View:**5993

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# Search Results for: topics-in-algebraic-and-topological-k-theory-lecture-notes-in-mathematics

**Author**: Paul Frank Baum,Ralf Meyer,Rubén Sánchez-García,Marco Schlichting,Bertrand Toën

**Publisher:** Springer Science & Business Media

**ISBN:** 3642157076

**Category:** Mathematics

**Page:** 308

**View:** 5993

This volume is an introductory textbook to K-theory, both algebraic and topological, and to various current research topics within the field, including Kasparov's bivariant K-theory, the Baum-Connes conjecture, the comparison between algebraic and topological K-theory of topological algebras, the K-theory of schemes, and the theory of dg-categories.
*Analytic and Geometric Structures*

**Author**: Jochen Brüning,Matthias Staudacher

**Publisher:** Walter de Gruyter GmbH & Co KG

**ISBN:** 3110452154

**Category:** Mathematics

**Page:** 517

**View:** 8768

This monograph describes some of the most interesting results obtained by the mathematicians and physicists collaborating in the CRC 647 "Space – Time – Matter", in the years 2005 - 2016. The work presented concerns the mathematical and physical foundations of string and quantum field theory as well as cosmology. Important topics are the spaces and metrics modelling the geometry of matter, and the evolution of these geometries. The partial differential equations governing such structures and their singularities, special solutions and stability properties are discussed in detail. Contents Introduction Algebraic K-theory, assembly maps, controlled algebra, and trace methods Lorentzian manifolds with special holonomy – Constructions and global properties Contributions to the spectral geometry of locally homogeneous spaces On conformally covariant differential operators and spectral theory of the holographic Laplacian Moduli and deformations Vector bundles in algebraic geometry and mathematical physics Dyson–Schwinger equations: Fix-point equations for quantum fields Hidden structure in the form factors ofN = 4 SYM On regulating the AdS superstring Constraints on CFT observables from the bootstrap program Simplifying amplitudes in Maxwell-Einstein and Yang-Mills-Einstein supergravities Yangian symmetry in maximally supersymmetric Yang-Mills theory Wave and Dirac equations on manifolds Geometric analysis on singular spaces Singularities and long-time behavior in nonlinear evolution equations and general relativity

**Author**: Jan de Gier,Cheryl E. Praeger,Terence Tao

**Publisher:** Springer

**ISBN:** 3319722999

**Category:** Mathematics

**Page:** 656

**View:** 7338

MATRIX is Australia’s international, residential mathematical research institute. It facilitates new collaborations and mathematical advances through intensive residential research programs, each lasting 1-4 weeks. This book is a scientific record of the five programs held at MATRIX in its first year, 2016: Higher Structures in Geometry and Physics (Chapters 1-5 and 18-21); Winter of Disconnectedness (Chapter 6 and 22-26); Approximation and Optimisation (Chapters 7-8); Refining C*-Algebraic Invariants for Dynamics using KK-theory (Chapters 9-13); Interactions between Topological Recursion, Modularity, Quantum Invariants and Low-dimensional Topology (Chapters 14-17 and 27). The MATRIX Scientific Committee selected these programs based on their scientific excellence and the participation rate of high-profile international participants. Each program included ample unstructured time to encourage collaborative research; some of the longer programs also included an embedded conference or lecture series. The articles are grouped into peer-reviewed contributions and other contributions. The peer-reviewed articles present original results or reviews on selected topics related to the MATRIX program; the remaining contributions are predominantly lecture notes based on talks or activities at MATRIX.

**Author**: Jonathan Rosenberg

**Publisher:** Springer Science & Business Media

**ISBN:** 9780387942483

**Category:** Mathematics

**Page:** 394

**View:** 9533

Algebraic K-Theory is crucial in many areas of modern mathematics, especially algebraic topology, number theory, algebraic geometry, and operator theory. This text is designed to help graduate students in other areas learn the basics of K-Theory and get a feel for its many applications. Topics include algebraic topology, homological algebra, algebraic number theory, and an introduction to cyclic homology and its interrelationship with K-Theory.

**Author**: James Frederic Davis,Paul Kirk

**Publisher:** American Mathematical Soc.

**ISBN:** 0821821601

**Category:** Mathematics

**Page:** 367

**View:** 2573

The amount of algebraic topology a graduate student specializing in topology must learn can be intimidating. Moreover, by their second year of graduate studies, students must make the transition from understanding simple proofs line-by-line to understanding the overall structure of proofs of difficult theorems. To help students make this transition, the material in this book is presented in an increasingly sophisticated manner. It is intended to bridge the gap between algebraic and geometric topology, both by providing the algebraic tools that a geometric topologist needs and by concentrating on those areas of algebraic topology that are geometrically motivated. Prerequisites for using this book include basic set-theoretic topology, the definition of CW-complexes, some knowledge of the fundamental group/covering space theory, and the construction of singular homology. Most of this material is briefly reviewed at the beginning of the book. The topics discussed by the authors include typical material for first- and second-year graduate courses. The core of the exposition consists of chapters on homotopy groups and on spectral sequences. There is also material that would interest students of geometric topology (homology with local coefficients and obstruction theory) and algebraic topology (spectra and generalized homology), as well as preparation for more advanced topics such as algebraic $K$-theory and the s-cobordism theorem. A unique feature of the book is the inclusion, at the end of each chapter, of several projects that require students to present proofs of substantial theorems and to write notes accompanying their explanations. Working on these projects allows students to grapple with the ``big picture'', teaches them how to give mathematical lectures, and prepares them for participating in research seminars. The book is designed as a textbook for graduate students studying algebraic and geometric topology and homotopy theory. It will also be useful for students from other fields such as differential geometry, algebraic geometry, and homological algebra. The exposition in the text is clear; special cases are presented over complex general statements.

**Author**: Eric Friedlander,Daniel R. Grayson

**Publisher:** Springer Science & Business Media

**ISBN:** 354023019X

**Category:** Mathematics

**Page:** 626

**View:** 5256

This handbook offers a compilation of techniques and results in K-theory. Each chapter is dedicated to a specific topic and is written by a leading expert. Many chapters present historical background; some present previously unpublished results, whereas some present the first expository account of a topic; many discuss future directions as well as open problems. It offers an exposition of our current state of knowledge as well as an implicit blueprint for future research.

**Author**: Vasudevan Srinivas

**Publisher:** Springer Science & Business Media

**ISBN:** 0817647368

**Category:** Mathematics

**Page:** 341

**View:** 9020

Algebraic K-Theory has become an increasingly active area of research. With its connections to algebra, algebraic geometry, topology, and number theory, it has implications for a wide variety of researchers and students in mathematics. This book is based on lectures given by the author at the Tata Institute in Bombay and elsewhere. This new edition includes an appendix on algebraic geometry that contains required definitions and results needed to understand the core of the book.
*The Equivariant Künneth Theorem in K-Theory. Dyer-Lashof operations in K-Theory*

**Author**: L.H. Hodgkin,V.P. Snaith

**Publisher:** Springer

**ISBN:** 3540380264

**Category:** Mathematics

**Page:** 294

**View:** 9363

**Author**: Elias Milnor,John Willard Milnor,Milnor John,John N. Mather

**Publisher:** Princeton University Press

**ISBN:** 9780691081014

**Category:** Mathematics

**Page:** 184

**View:** 2032

Algebraic K-theory describes a branch of algebra that centers about two functors. K0 and K1, which assign to each associative ring ∧ an abelian group K0∧ or K1∧ respectively. Professor Milnor sets out, in the present work, to define and study an analogous functor K2, also from associative rings to abelian groups. Just as functors K0 and K1 are important to geometric topologists, K2 is now considered to have similar topological applications. The exposition includes, besides K-theory, a considerable amount of related arithmetic.

**Author**: James F. Davis and Paul Kirk

**Publisher:** American Mathematical Soc.

**ISBN:** 9780821872208

**Category:**

**Page:** N.A

**View:** 1866

**Author**: Richard G. Swan

**Publisher:** Springer

**ISBN:** 3540359176

**Category:** Mathematics

**Page:** 264

**View:** 2601

From the Introduction: "These notes are taken from a course on algebraic K-theory [given] at the University of Chicago in 1967. They also include some material from an earlier course on abelian categories, elaborating certain parts of Gabriel's thesis. The results on K-theory are mostly of a very general nature."
*Homologie und Mannigfaltigkeiten*

**Author**: Wolfgang Lück

**Publisher:** Springer-Verlag

**ISBN:** 3322802418

**Category:** Mathematics

**Page:** 266

**View:** 6592

Hauptgegenstand des Buches sind Homologie-, Kohomologietheorien und Mannigfaltigkeiten. In den ersten acht Kapiteln werden Begriffe wie Homologie, CW-Komplexe, Produkte und Poincaré Dualität eingeführt und deren Anwendungen diskutiert. In den davon unabhängigen Kapiteln 9 bis 13 werden Differentialformen und der Satz von Stokes auf Mannigfaltigkeiten behandelt. Die in Kapitel 14 und 15 behandelte de Rham Kohomologie und der Satz von de Rham verbinden diese beiden Teile.

**Author**: M. Rørdam,Flemming Larsen,N. Laustsen

**Publisher:** Cambridge University Press

**ISBN:** 9780521789448

**Category:** Mathematics

**Page:** 242

**View:** 9766

This book provides a very elementary introduction to K-theory for C*-algebras, and is ideal for beginning graduate students.
*Volume 2: K-Theory*

**Author**: Michael Atiyah

**Publisher:** Oxford University Press

**ISBN:** 9780198532767

**Category:** Language Arts & Disciplines

**Page:** 854

**View:** 8217

One of the greatest mathematicians in the world, Michael Atiyah has earned numerous honors, including a Fields Medal, the mathematical equivalent of the Nobel Prize. While the focus of his work has been in the areas of algebraic geometry and topology, he has also participated in research with theoretical physicists. For the first time, these volumes bring together Atiyah's collected papers--both monographs and collaborative works-- including those dealing with mathematical education and current topics of research such as K-theory and gauge theory. The volumes are organized thematically. They will be of great interest to research mathematicians, theoretical physicists, and graduate students in these areas.
*proceedings of a conference held at Rutgers University, New Brunswick, USA, July 6-13, 1983*

**Author**: Andrew Ranicki,Norman Levitt,Frank Quinn

**Publisher:** Egully.com

**ISBN:** 9783540152354

**Category:** Mathematics

**Page:** 423

**View:** 3930

**Author**: Jean Pierre Serre

**Publisher:** Springer-Verlag

**ISBN:** 3322858634

**Category:** Mathematics

**Page:** 102

**View:** 579

**Author**: Friedrich Hirzebruch

**Publisher:** Springer-Verlag

**ISBN:** 3663140458

**Category:** Mathematics

**Page:** 212

**View:** 743

*proceedings of the international conference held at Bielefeld, Federal Republic of Germany, July 26-30, 1982*

**Author**: Anthony Bak

**Publisher:** N.A

**ISBN:** 9783540128915

**Category:** Algebraic number theory

**Page:** 464

**View:** 3532

*die Geschichte eines mathematischen Abenteuers*

**Author**: Donal O'Shea

**Publisher:** N.A

**ISBN:** 9783596176632

**Category:**

**Page:** 376

**View:** 8584

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